2001/08/31 by P. L. Krapivsky, E. Ben-Naim, E. Ben‐Naim +2
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Statistical Distribution Estimation and Applications #Stochastic processes and statistical mechanics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/37/8/002
published as J. Phys. A 37, 2863 (2004) · 11 pages, 5 figures
arxiv created 2001/08/31 · openalex publication_date 2004/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail. Furthermore, the entire range of acceptable values of decay exponent consistent with length conservation can be realized. We show that the stochastic fragmentation process is non-self-averaging as moments exhibit significant sample-to-sample fluctuations. Additionally, we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities.